We will also employ the following Bernoulli bond percolation result. Lemma REF  summarizes a combination of standard results in Bernoulli bond percolation theory (see [1]}, [2]}, [3]}, [4]}, [5]}). We underline that the choice of the origin \(J=0\)  in the following statement plays no role. In particular (REF ),(REF ) remain valid for a generic \(J\) .
